An Enhanced Smoothing Algorithm for MPM to Stabilize Hydrodynamic Impact Problems with Embedded Solids

Abstract

The impact of debris carried by floods or tsunamis can cause severe damage to structures, but the complex phenomena involved are difficult to model. The Material Point Method (MPM) provides one framework for modeling such systems, with the capability of incorporating combined fluid/solid behavior with complex interaction. Conventional MPM uses regular grids with tri-linear interpolation. However, linear functions introduce volumetric locking for (nearly) incompressible materials, posing problems when modeling liquids. To eliminate locking, hybrid formulations similar to those used with finite elements were adapted by Mast et al. [1]. This approach introduced two classes of anti-locking algorithms for nearly incompressible materials: a cell-based and a node-based variant. Both variants filter incompatible strains and stresses, but also affect the stability of the time integration. For hydrodynamic problems the cell-based algorithm is prone to checker-board stress fields, while the node-based algorithm can introduce excessive dissipation. This paper presents a new numerical flux smoothing algorithm to produce smooth stress fields in complex hydrodynamic problems while enhancing numerical stability. The goal is to combine the stability of the node-based anti-locking approach with the cell-based variant's capability to effectively solve hydrostatic problems. The improved algorithm is validated using a hydrostatic problem to isolate and minimize the effect of integration errors. A complex hydrodynamic problem involving an embedded solid block is then used as an example to display the new algorithm's modeling capabilities.